Gay-Lussac's law: absolute zero
Verify Gay-Lussac's law (P proportional to T at constant volume) and estimate absolute zero with the FizziQ Web Ideal Gas simulation.
Activity Summary
The student uses the FizziQ Web Ideal Gas simulation with the piston fixed (constant volume). They slowly vary the temperature while recording pressure and temperature simultaneously. By plotting P versus T and extrapolating to P = 0, they estimate absolute zero.
Introduction
What happens when you heat a gas trapped in a rigid container? The pressure increases! But how exactly? In 1802, Joseph Louis Gay-Lussac discovered that the pressure of a gas at constant volume is directly proportional to its absolute temperature. This seemingly simple law has a profound implication: if you extrapolate the pressure-temperature line back to zero pressure, you find a temperature below which the gas cannot exist — absolute zero. The FizziQ Web Ideal Gas simulation lets you verify this law and estimate this fundamental temperature using nothing more than a virtual thermometer and pressure gauge.
Learning Objectives
- Record pressure and temperature simultaneously during an isochoric transformation
- Plot P versus T and verify the linear relationship
- Estimate absolute zero by extrapolating the P(T) graph to P = 0
- Understand the connection between Gay-Lussac's law and the ideal gas law
Scientific Concepts
Instruments and sensors
Scientific instruments
- FizziQ Web Ideal Gas simulation
FizziQ Features
- Experiment notebook — records the simultaneous pressure and temperature readings, plots P versus T, and exports the data for the extrapolation to absolute zero.
Required Materials
- - Computer, tablet, or smartphone with FizziQ Web - Note: the protocol remains adaptable to any comparable simulation or data-plotting tool.
Experimental Protocol
Open the Ideal Gas simulation in FizziQ Web. Position the piston at mid-stroke and do not touch it for the entire experiment.
Select the quantities to record: enable Pressure and Temperature.
Set the temperature to the minimum (273 K = 0°C). Note the corresponding pressure.
Click REC to start recording. Slowly increase the temperature from 273 K to 333 K (60°C) by moving the temperature slider gradually.
Stop the recording. The P and T data are exported to the experiment notebook.
Plot the graph of P versus T (in kelvin). Is the curve a straight line?
Calculate the ratio P/T for several data points. Is this ratio constant?
If you plotted P(T) in kelvin, the line should pass through the origin. If you plot P versus temperature in °C, at what negative temperature does the line cross P = 0?
Extrapolate the P(T in °C) line to P = 0. At what temperature does the line cross the axis? This value is an estimate of absolute zero.
Compare your value with the theoretical absolute zero (-273.15°C = 0 K). Write a conclusion about the relationship between pressure and absolute temperature.
Expected Results
The graph P(T in kelvin) is a straight line through the origin, confirming P = (nR/V) × T. The ratio P/T is constant for all measurements. When plotted in °C, the line crosses the P = 0 axis at approximately -273°C, providing an experimental estimate of absolute zero. The precision depends on the range of temperatures explored and the linearity of the data.
Scientific Questions
- What would physically happen if you could cool a gas down to absolute zero?
- How can you verify that the volume truly stayed constant during the experiment?
- Why does the graph P(T in °C) not pass through the origin while P(T in K) does?
- What is the physical meaning of the slope of the P(T) line?
- How would the graph change if you repeated the experiment at a different (but still constant) volume?
Scientific Background
**Gay-Lussac's law** states that for a gas at constant volume, the pressure is proportional to the absolute temperature: **P = (nR/V) × T**. This means that doubling the absolute temperature doubles the pressure.
This law is a direct consequence of the ideal gas law PV = nRT, when V, n, and R are held constant. The pressure increases because the gas molecules move faster at higher temperatures and hit the container walls harder and more frequently.
**Absolute zero** (0 K = -273.15°C) is the temperature at which molecular motion would theoretically cease. The pressure would drop to zero because there would be no molecular impacts on the walls. In reality, quantum effects prevent reaching exactly 0 K.
The **kelvin scale** is defined from absolute zero: T(K) = T(°C) + 273.15. It is the natural scale for gas laws because proportionality relationships only hold with absolute temperature.
This simulation is the digital counterpart of a real experiment with a barometer in a jar. The advantage is the ability to explore a wider temperature range and eliminate experimental noise.
Extensions
- Compare the simulation results with those from a real experiment using a smartphone barometer
- Calculate the number of moles n from the slope and the known volume
- Investigate what happens if the piston is not perfectly fixed during the experiment
- Estimate absolute zero from only two data points and evaluate the precision compared to using the full dataset
Frequently Asked Questions
The straight line does not pass exactly through the origin in kelvin.
Check that the volume truly stayed constant (the piston did not move). If you moved the piston during recording, the data points will not follow a single straight line.
My estimate of absolute zero is not exactly -273°C.
This is normal. The precision depends on the temperature range you explored and measurement accuracy. An estimate between -260°C and -280°C is a good result.
Why use kelvin instead of Celsius?
The proportionality P ∝ T only holds in kelvin. In Celsius, the relationship is P = a × (T + 273), which is linear but does not pass through the origin.
Can I do this experiment with a real gas?
Yes, using a sealed container, a pressure sensor, and a temperature probe. The smartphone barometer can serve as the pressure sensor. The results match the simulation for moderate temperatures and pressures.
Detailed Description
The student uses the FizziQ Web Ideal Gas simulation with the piston fixed (constant volume). They slowly vary the temperature while recording pressure and temperature simultaneously. By plotting P versus T and extrapolating to P = 0, they estimate absolute zero. FizziQ Web runs the simulation directly in the browser and its experiment notebook records, plots, and exports the paired pressure/temperature readings needed for the P(T) analysis.
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